Subgroups — C₃×#60495 #10679102

Order 768.

2090 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
3	C₃×#3084	C₂	1	6	yes	maximal, complemented
4	C₃×#3081	C₂	1	6	yes	maximal, complemented
5	C₃×#3079	C₂	1	3	yes	maximal, complemented
6	C₃×#3077	C₂	1	3	yes	maximal, complemented
7	C₃×#3076	C₂	1	3	yes	maximal, complemented
8	C₂×C₃×#476	C₂	1	3	yes	maximal, complemented
9	C₃×#2912	C₂	1	2	yes	maximal, complemented
10	C₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2897	C₂	1	2	yes	maximal
12	#60495	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂×C₃×#131	C₂²	1	2	yes	—
15	C₃×Q₈²	—	2	1	no	—
16	C₃×#557	—	2	1	no	—
17	C₃×#554	—	2	3	no	—
18	C₃×D₄×Q₈	—	2	3	no	—
19	C₃×#544	C₂²	1	6	yes	complemented
20	C₃×#533	C₂²	1	3	yes	complemented
21	C₂×C₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
22	C₃×#520	—	2	1	no	—
23	C₃×#520	C₂²	1	3	yes	—
24	C₃×#520	C₂²	1	1	yes	characteristic
25	C₃×#520	C₂²	1	2	yes	—
26	C₃×#518	—	2	3	no	—
27	C₃×#518	C₂²	1	3	yes	—
28	C₃×C₄×#41	—	2	1	no	—
29	C₃×C₄×#41	C₂²	1	3	yes	—
30	C₃×C₄×#41	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₄	—	2	3	no	—
32	C₂×C₃×C₄×D₄	C₂²	1	3	yes	—
33	C₃×#479	C₂²	1	6	yes	complemented
34	C₃×#478	C₂²	1	6	yes	complemented
35	C₃×#478	C₂²	1	12	yes	complemented
36	C₃×#477	C₂²	1	3	yes	complemented
37	C₃×#476	C₂²	1	3	yes	complemented
38	C₃×#476	C₂²	1	6	yes	complemented
39	C₃×#476	C₂²	1	12	yes	complemented
40	C₃×#475	C₂²	1	1	yes	characteristic, complemented
41	C₃×#475	C₂²	1	6	yes	complemented
42	C₃×#474	C₂²	1	3	yes	complemented
43	C₃×#474	C₂²	1	6	yes	complemented
44	C₃×#428	C₂²	1	6	yes	complemented
45	C₃×#428	C₂²	1	6	yes	complemented
46	C₃×#427	C₂²	1	6	yes	complemented
47	C₂×C₃×#106	C₂²	1	6	yes	complemented
48	C₃×#424	C₂²	1	6	yes	complemented
49	C₃×#423	C₂²	1	3	yes	complemented
50	C₂×C₃×C₄⋊C₈	C₂²	1	3	yes	complemented
51	C₃×#418	C₂²	1	6	yes	—
52	C₃×#417	C₂²	1	6	yes	—
53	C₃×#416	C₂²	1	6	yes	—
54	C₂×C₃×#102	C₂²	1	6	yes	—
55	#3503	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
57	#3084	C₂×C₃	1	6	yes	complemented
58	#3081	C₂×C₃	1	6	yes	complemented
59	#3079	C₂×C₃	1	3	yes	complemented
60	#3077	C₂×C₃	1	3	yes	complemented
61	#3076	C₂×C₃	1	3	yes	complemented
62	C₂×#476	C₂×C₃	1	3	yes	complemented
63	#2912	C₂×C₃	1	2	yes	complemented
64	#2906	C₂×C₃	1	1	yes	characteristic, complemented
65	#2897	C₂×C₃	1	2	yes	—
66	C₃×H(5,𝔽₂)	—	2	4	no	—
67	C₃×H(5,𝔽₂)	Q₈	1	8	yes	complemented
68	C₂×C₃×#41	—	2	1	no	—
69	C₂×C₃×#41	C₂³	1	3	yes	—
70	C₂×C₃×#41	C₂³	1	1	yes	characteristic
71	C₂²×C₃×Q₈	—	2	3	no	—
72	C₂²×C₃×D₄	—	2	3	no	—
73	C₂²×C₃×D₄	C₂³	1	3	yes	—
74	C₂³×C₃×C₄	—	2	3	no	—
75	C₃×#131	—	2	8	no	—
76	C₂×C₃×M₁₆	C₂³	1	6	yes	—
77	C₂²×C₃×C₈	C₂³	1	6	yes	—
78	C₃×C₄⋊Q₈	—	2	6	no	—
79	C₃×C₄⋊Q₈	—	2	3	no	—
80	C₃×C₄⋊Q₈	—	2	3	no	—
81	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
83	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
84	C₃×#125	—	2	6	no	—
85	C₃×#125	C₂³	1	6	yes	—
86	C₃×C₂²⋊Q₈	—	2	3	no	—
87	C₃×C₂²⋊Q₈	—	2	3	no	—
88	C₃×C₂²⋊Q₈	—	2	12	no	—
89	C₃×C₄×Q₈	—	2	2	no	—
90	C₃×C₄×Q₈	—	2	1	no	—
91	C₃×C₄×Q₈	—	2	3	no	—
92	C₃×C₄×Q₈	—	2	3	no	—
93	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
94	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
95	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
96	C₃×C₄×Q₈	C₂³	1	3	yes	—
97	C₃×C₄×D₄	—	2	3	no	—
98	C₃×C₄×D₄	—	2	6	no	—
99	C₃×C₄×D₄	—	2	3	no	—
100	C₃×C₄×D₄	—	2	3	no	—
101	C₃×C₄×D₄	—	2	3	no	—
102	C₃×C₄×D₄	—	2	3	no	—
103	C₃×C₄×D₄	—	2	6	no	—
104	C₃×C₄×D₄	—	2	3	no	—
105	C₃×C₄×D₄	—	2	3	no	—
106	C₃×C₄×D₄	D₄	1	3	yes	—
107	C₃×C₄×D₄	D₄	1	3	yes	—
108	C₃×C₄×D₄	C₂³	1	3	yes	—
109	C₃×C₄×D₄	C₂³	1	6	yes	—
110	C₃×C₄×D₄	C₂³	1	3	yes	—
111	C₃×#117	—	2	3	no	—
112	C₃×#117	—	2	3	no	—
113	C₃×#117	C₂³	1	6	yes	—
114	C₃×#117	C₂³	1	3	yes	—
115	C₃×#117	C₂³	1	3	yes	—
116	C₂×C₃×C₄⋊C₄	—	2	3	no	—
117	C₂×C₃×C₄⋊C₄	—	2	3	no	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
119	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
120	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
121	C₂×C₃×C₂²⋊C₄	—	2	6	no	—
122	C₂×C₃×C₄²	—	2	3	no	—
123	C₂×C₃×C₄²	C₂³	1	3	yes	—
124	C₃×#107	C₂³	1	6	yes	—
125	C₃×#107	C₂³	1	6	yes	—
126	C₃×#106	C₂³	1	6	yes	—
127	C₃×#106	C₂³	1	12	yes	—
128	C₃×#106	C₂³	1	2	yes	—
129	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂³	1	3	yes	—
131	C₃×C₄⋊C₈	C₂³	1	6	yes	—
132	C₃×C₄⋊C₈	C₂³	1	6	yes	—
133	C₃×#103	C₂³	1	2	yes	—
134	C₃×#103	C₂³	1	6	yes	—
135	C₃×#102	C₂³	1	6	yes	—
136	C₃×#102	C₂³	1	12	yes	—
137	C₃×#102	C₂³	1	6	yes	—
138	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
139	C₂×#131	C₂²×C₃	1	2	yes	—
140	Q₈²	—	2	1	no	—
141	#557	—	2	1	no	—
142	#554	—	2	3	no	—
143	D₄×Q₈	—	2	3	no	—
144	#544	C₂²×C₃	1	6	yes	complemented
145	#533	C₂²×C₃	1	3	yes	complemented
146	C₂×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
147	#520	—	2	1	no	—
148	#520	C₂²×C₃	1	3	yes	—
149	#520	C₂²×C₃	1	2	yes	—
150	#520	C₂²×C₃	1	1	yes	characteristic
151	#518	—	2	3	no	—
152	#518	C₂²×C₃	1	3	yes	—
153	C₄×#41	—	2	1	no	—
154	C₄×#41	C₂²×C₃	1	3	yes	—
155	C₄×#41	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₄×D₄	—	2	3	no	—
157	C₂×C₄×D₄	C₂²×C₃	1	3	yes	—
158	#479	C₂²×C₃	1	6	yes	complemented
159	#478	C₂²×C₃	1	6	yes	complemented
160	#478	C₂²×C₃	1	12	yes	complemented
161	#477	C₂²×C₃	1	3	yes	complemented
162	#476	C₂²×C₃	1	3	yes	complemented
163	#476	C₂²×C₃	1	6	yes	complemented
164	#476	C₂²×C₃	1	12	yes	complemented
165	#475	C₂²×C₃	1	1	yes	characteristic, complemented
166	#475	C₂²×C₃	1	6	yes	complemented
167	#474	C₂²×C₃	1	3	yes	complemented
168	#474	C₂²×C₃	1	6	yes	complemented
169	#428	C₂²×C₃	1	6	yes	complemented
170	#428	C₂²×C₃	1	6	yes	complemented
171	#427	C₂²×C₃	1	6	yes	complemented
172	C₂×#106	C₂²×C₃	1	6	yes	complemented
173	#424	C₂²×C₃	1	6	yes	complemented
174	#423	C₂²×C₃	1	3	yes	complemented
175	C₂×C₄⋊C₈	C₂²×C₃	1	3	yes	complemented
176	#418	C₂²×C₃	1	6	yes	—
177	#417	C₂²×C₃	1	6	yes	—
178	#416	C₂²×C₃	1	6	yes	—
179	C₂×#102	C₂²×C₃	1	6	yes	—
180	C₂⁴×C₃	—	2	3	no	—
181	C₃×#41	—	2	8	no	—
182	C₃×#41	—	2	6	no	—
183	C₃×#41	C₂×Q₈	1	4	yes	—
184	C₃×#41	C₂×Q₈	1	12	yes	complemented
185	C₃×#41	#41	1	4	yes	—
186	C₂×C₃×Q₈	—	2	1	no	—
187	C₂×C₃×Q₈	—	2	3	no	—
188	C₂×C₃×Q₈	—	2	6	no	—
189	C₂×C₃×Q₈	—	8	6	no	—
190	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
192	C₂×C₃×D₄	—	2	3	no	—
193	C₂×C₃×D₄	—	2	24	no	—
194	C₂×C₃×D₄	—	2	3	no	—
195	C₂×C₃×D₄	—	2	6	no	—
196	C₂×C₃×D₄	C₂×D₄	1	3	yes	—
197	C₂×C₃×D₄	C₂×Q₈	1	12	yes	complemented
198	C₂×C₃×D₄	C₂⁴	1	3	yes	—
199	C₂²×C₃×C₄	—	2	3	no	—
200	C₂²×C₃×C₄	—	2	3	no	—
201	C₂²×C₃×C₄	—	2	6	no	—
202	C₂²×C₃×C₄	—	2	3	no	—
203	C₂²×C₃×C₄	—	2	3	no	—
204	C₂²×C₃×C₄	—	2	6	no	—
205	C₂²×C₃×C₄	—	8	6	no	—
206	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
207	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
208	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
209	C₃×M₁₆	—	2	12	no	—
210	C₂×C₃×C₈	—	2	12	no	—
211	C₂×C₃×C₈	C₂⁴	1	2	yes	—
212	C₂×C₃×C₈	C₂⁴	1	6	yes	—
213	C₃×C₄⋊C₄	—	2	3	no	—
214	C₃×C₄⋊C₄	—	2	3	no	—
215	C₃×C₄⋊C₄	—	2	3	no	—
216	C₃×C₄⋊C₄	—	2	6	no	—
217	C₃×C₄⋊C₄	—	2	6	no	—
218	C₃×C₄⋊C₄	—	2	1	no	—
219	C₃×C₄⋊C₄	—	2	1	no	—
220	C₃×C₄⋊C₄	—	2	6	no	—
221	C₃×C₄⋊C₄	—	2	6	no	—
222	C₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
223	C₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
224	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
225	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
226	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
227	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
228	C₃×C₂²⋊C₄	—	2	3	no	—
229	C₃×C₂²⋊C₄	—	2	6	no	—
230	C₃×C₂²⋊C₄	—	2	3	no	—
231	C₃×C₂²⋊C₄	—	2	6	no	—
232	C₃×C₂²⋊C₄	—	2	3	no	—
233	C₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
234	C₃×C₄²	—	2	1	no	—
235	C₃×C₄²	—	2	3	no	—
236	C₃×C₄²	—	2	3	no	—
237	C₃×C₄²	—	2	6	no	—
238	C₃×C₄²	C₂×D₄	1	3	yes	—
239	C₃×C₄²	C₂×D₄	1	3	yes	—
240	C₃×C₄²	C₂⁴	1	1	yes	characteristic
241	C₃×C₄²	C₂⁴	1	3	yes	—
242	H(5,𝔽₂)	—	2	4	no	—
243	H(5,𝔽₂)	C₃×Q₈	1	8	yes	complemented
244	C₂×#41	—	2	1	no	—
245	C₂×#41	C₂³×C₃	1	3	yes	—
246	C₂×#41	C₂³×C₃	1	1	yes	characteristic
247	C₂²×Q₈	—	2	3	no	—
248	C₂²×D₄	—	2	3	no	—
249	C₂²×D₄	C₂³×C₃	1	3	yes	—
250	C₂³×C₄	—	2	3	no	—
251	#131	—	2	8	no	—
252	C₂×M₁₆	C₂³×C₃	1	6	yes	—
253	C₂²×C₈	C₂³×C₃	1	6	yes	—
254	C₄⋊Q₈	—	2	6	no	—
255	C₄⋊Q₈	—	2	3	no	—
256	C₄⋊Q₈	—	2	3	no	—
257	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
258	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
259	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
260	#125	—	2	6	no	—
261	#125	C₂³×C₃	1	6	yes	—
262	C₂²⋊Q₈	—	2	3	no	—
263	C₂²⋊Q₈	—	2	3	no	—
264	C₂²⋊Q₈	—	2	12	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	3	no	—
268	C₄×Q₈	—	2	3	no	—
269	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
270	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
271	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
272	C₄×Q₈	C₂³×C₃	1	3	yes	—
273	C₄×D₄	—	2	3	no	—
274	C₄×D₄	—	2	6	no	—
275	C₄×D₄	—	2	3	no	—
276	C₄×D₄	—	2	3	no	—
277	C₄×D₄	—	2	3	no	—
278	C₄×D₄	—	2	3	no	—
279	C₄×D₄	—	2	6	no	—
280	C₄×D₄	—	2	3	no	—
281	C₄×D₄	—	2	3	no	—
282	C₄×D₄	C₃×D₄	1	3	yes	—
283	C₄×D₄	C₃×D₄	1	3	yes	—
284	C₄×D₄	C₂³×C₃	1	3	yes	—
285	C₄×D₄	C₂³×C₃	1	6	yes	—
286	C₄×D₄	C₂³×C₃	1	3	yes	—
287	#117	—	2	3	no	—
288	#117	—	2	3	no	—
289	#117	C₂³×C₃	1	3	yes	—
290	#117	C₂³×C₃	1	6	yes	—
291	#117	C₂³×C₃	1	3	yes	—
292	C₂×C₄⋊C₄	—	2	3	no	—
293	C₂×C₄⋊C₄	—	2	3	no	—
294	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
295	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
296	C₂×C₂²⋊C₄	—	2	3	no	—
297	C₂×C₂²⋊C₄	—	2	6	no	—
298	C₂×C₄²	—	2	3	no	—
299	C₂×C₄²	C₂³×C₃	1	3	yes	—
300	#107	C₂³×C₃	1	6	yes	—
301	#107	C₂³×C₃	1	6	yes	—
302	#106	C₂³×C₃	1	6	yes	—
303	#106	C₂³×C₃	1	12	yes	—
304	#106	C₂³×C₃	1	2	yes	—
305	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₃	1	3	yes	—
307	C₄⋊C₈	C₂³×C₃	1	6	yes	—
308	C₄⋊C₈	C₂³×C₃	1	6	yes	—
309	#103	C₂³×C₃	1	2	yes	—
310	#103	C₂³×C₃	1	6	yes	—
311	#102	C₂³×C₃	1	6	yes	—
312	#102	C₂³×C₃	1	12	yes	—
313	#102	C₂³×C₃	1	6	yes	—
314	C₂³×C₃	—	2	3	no	—
315	C₂³×C₃	—	2	12	no	—
316	C₂³×C₃	—	8	3	no	—
317	C₂³×C₃	—	8	3	no	—
318	C₂³×C₃	C₂²×D₄	1	3	yes	—
319	C₃×Q₈	—	2	1	no	—
320	C₃×Q₈	—	4	6	no	—
321	C₃×Q₈	—	4	2	no	—
322	C₃×Q₈	—	8	6	no	—
323	C₃×Q₈	C₂²⋊Q₈	1	4	yes	—
324	C₃×Q₈	C₂²×Q₈	1	2	yes	—
325	C₃×D₄	—	2	12	no	—
326	C₃×D₄	—	2	12	no	—
327	C₃×D₄	—	2	3	no	—
328	C₃×D₄	C₂²⋊Q₈	1	12	yes	—
329	C₃×D₄	C₂²×Q₈	1	6	yes	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	12	no	—
332	C₂×C₃×C₄	—	2	6	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	3	no	—
336	C₂×C₃×C₄	—	2	6	no	—
337	C₂×C₃×C₄	—	4	3	no	—
338	C₂×C₃×C₄	—	4	6	no	—
339	C₂×C₃×C₄	—	8	3	no	—
340	C₂×C₃×C₄	—	8	6	no	—
341	C₂×C₃×C₄	—	8	3	no	—
342	C₂×C₃×C₄	—	8	6	no	—
343	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
344	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
346	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
347	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂²×Q₈	1	6	yes	—
349	C₂×C₃×C₄	C₂×#41	1	6	yes	—
350	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
351	C₃×C₈	—	2	2	no	—
352	C₃×C₈	—	2	6	no	—
353	C₂⁴	—	2	3	no	—
354	#41	—	2	8	no	—
355	#41	—	2	6	no	—
356	#41	C₂×C₃×Q₈	1	4	yes	—
357	#41	C₂×C₃×Q₈	1	12	yes	complemented
358	#41	C₃×#41	1	4	yes	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	3	no	—
361	C₂×Q₈	—	2	6	no	—
362	C₂×Q₈	—	8	6	no	—
363	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
364	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	2	24	no	—
367	C₂×D₄	—	2	3	no	—
368	C₂×D₄	—	2	6	no	—
369	C₂×D₄	C₂×C₃×D₄	1	3	yes	—
370	C₂×D₄	C₂×C₃×Q₈	1	12	yes	complemented
371	C₂×D₄	C₂⁴×C₃	1	3	yes	—
372	C₂²×C₄	—	2	3	no	—
373	C₂²×C₄	—	2	3	no	—
374	C₂²×C₄	—	2	6	no	—
375	C₂²×C₄	—	2	3	no	—
376	C₂²×C₄	—	2	3	no	—
377	C₂²×C₄	—	2	6	no	—
378	C₂²×C₄	—	8	6	no	—
379	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
380	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
381	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
382	M₁₆	—	2	12	no	—
383	C₂×C₈	—	2	12	no	—
384	C₂×C₈	C₂⁴×C₃	1	2	yes	—
385	C₂×C₈	C₂⁴×C₃	1	6	yes	—
386	C₄⋊C₄	—	2	3	no	—
387	C₄⋊C₄	—	2	3	no	—
388	C₄⋊C₄	—	2	3	no	—
389	C₄⋊C₄	—	2	6	no	—
390	C₄⋊C₄	—	2	6	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	6	no	—
395	C₄⋊C₄	C₂×C₃×D₄	1	3	yes	—
396	C₄⋊C₄	C₂×C₃×D₄	1	3	yes	—
397	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
398	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
399	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
400	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	3	no	—
402	C₂²⋊C₄	—	2	6	no	—
403	C₂²⋊C₄	—	2	3	no	—
404	C₂²⋊C₄	—	2	6	no	—
405	C₂²⋊C₄	—	2	3	no	—
406	C₂²⋊C₄	C₂×C₃×D₄	1	6	yes	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	3	no	—
409	C₄²	—	2	3	no	—
410	C₄²	—	2	6	no	—
411	C₄²	C₂×C₃×D₄	1	3	yes	—
412	C₄²	C₂×C₃×D₄	1	3	yes	—
413	C₄²	C₂⁴×C₃	1	1	yes	characteristic
414	C₄²	C₂⁴×C₃	1	3	yes	—
415	C₂²×C₃	—	2	3	no	—
416	C₂²×C₃	—	2	3	no	—
417	C₂²×C₃	—	2	6	no	—
418	C₂²×C₃	—	4	3	no	—
419	C₂²×C₃	—	4	3	no	—
420	C₂²×C₃	—	8	12	no	—
421	C₂²×C₃	C₂×C₂²⋊Q₈	1	6	yes	—
422	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	3	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	3	no	—
427	C₃×C₄	—	4	1	no	—
428	C₃×C₄	—	4	6	no	—
429	C₃×C₄	—	4	3	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	C₂×C₂²⋊Q₈	1	6	yes	—
432	C₃×C₄	#577	1	2	yes	—
433	C₃×C₄	C₂³×Q₈	1	1	yes	characteristic
434	C₃×C₄	C₂²×#41	1	1	yes	characteristic
435	C₂³	—	2	3	no	—
436	C₂³	—	2	12	no	—
437	C₂³	—	8	3	no	—
438	C₂³	—	8	3	no	—
439	C₂³	C₂²×C₃×D₄	1	3	yes	—
440	Q₈	—	2	1	no	—
441	Q₈	—	4	6	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	8	6	no	—
444	Q₈	C₃×C₂²⋊Q₈	1	4	yes	—
445	Q₈	C₂²×C₃×Q₈	1	2	yes	—
446	D₄	—	2	12	no	—
447	D₄	—	2	3	no	—
448	D₄	—	2	12	no	—
449	D₄	C₃×C₂²⋊Q₈	1	12	yes	—
450	D₄	C₂²×C₃×Q₈	1	6	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	6	no	—
453	C₂×C₄	—	2	12	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	3	no	—
457	C₂×C₄	—	2	6	no	—
458	C₂×C₄	—	4	3	no	—
459	C₂×C₄	—	4	6	no	—
460	C₂×C₄	—	8	6	no	—
461	C₂×C₄	—	8	3	no	—
462	C₂×C₄	—	8	3	no	—
463	C₂×C₄	—	8	6	no	—
464	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
465	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
467	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
469	C₂×C₄	C₂²×C₃×Q₈	1	6	yes	—
470	C₂×C₄	C₂×C₃×#41	1	6	yes	—
471	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	—	2	6	no	—
474	C₂×C₃	—	2	6	no	—
475	C₂×C₃	—	4	6	no	—
476	C₂×C₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
477	C₂×C₃	C₂×#577	1	1	yes	characteristic
478	C₂×C₃	#3585	1	1	yes	characteristic
479	C₂²	—	2	3	no	—
480	C₂²	—	2	3	no	—
481	C₂²	—	2	6	no	—
482	C₂²	—	4	3	no	—
483	C₂²	—	4	3	no	—
484	C₂²	—	8	12	no	—
485	C₂²	C₂×C₃×C₂²⋊Q₈	1	6	yes	—
486	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	3	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	3	no	—
491	C₄	—	4	3	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	6	no	—
495	C₄	C₂×C₃×C₂²⋊Q₈	1	6	yes	—
496	C₄	C₃×#577	1	2	yes	—
497	C₄	C₂³×C₃×Q₈	1	1	yes	characteristic
498	C₄	C₂²×C₃×#41	1	1	yes	characteristic
499	C₃	#60495	1	1	yes	characteristic, direct product factor, Sylow
500	C₂	—	2	6	no	—
501	C₂	—	4	6	no	—
502	C₂	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic
503	C₂	C₂×C₃×#577	1	1	yes	characteristic
504	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×#3503	C₂	semidirect
3. C₃×#3084	C₂	semidirect
4. C₃×#3081	C₂	semidirect
5. C₃×#3079	C₂	semidirect
6. C₃×#3077	C₂	semidirect
7. C₃×#3076	C₂	semidirect
8. C₂×C₃×#476	C₂	semidirect
9. C₃×#2912	C₂	semidirect
10. C₃×#2906	C₂	semidirect
12. #60495	C₃	direct (N × H)
19. C₃×#544	C₂²	semidirect
20. C₃×#533	C₂²	semidirect
21. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
33. C₃×#479	C₂²	semidirect
34. C₃×#478	C₂²	semidirect
35. C₃×#478	C₂²	semidirect
36. C₃×#477	C₂²	semidirect
37. C₃×#476	C₂²	semidirect
38. C₃×#476	C₂²	semidirect
39. C₃×#476	C₂²	semidirect
40. C₃×#475	C₂²	semidirect
41. C₃×#475	C₂²	semidirect
42. C₃×#474	C₂²	semidirect
43. C₃×#474	C₂²	semidirect
44. C₃×#428	C₂²	semidirect
45. C₃×#428	C₂²	semidirect
46. C₃×#427	C₂²	semidirect
47. C₂×C₃×#106	C₂²	semidirect
48. C₃×#424	C₂²	semidirect
49. C₃×#423	C₂²	semidirect
50. C₂×C₃×C₄⋊C₈	C₂²	semidirect
55. #3503	C₂×C₃	semidirect
57. #3084	C₂×C₃	semidirect
58. #3081	C₂×C₃	semidirect
59. #3079	C₂×C₃	semidirect
60. #3077	C₂×C₃	semidirect
61. #3076	C₂×C₃	semidirect
62. C₂×#476	C₂×C₃	semidirect
63. #2912	C₂×C₃	semidirect
64. #2906	C₂×C₃	semidirect
67. C₃×H(5,𝔽₂)	Q₈	semidirect
144. #544	C₂²×C₃	semidirect
145. #533	C₂²×C₃	semidirect
146. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
158. #479	C₂²×C₃	semidirect
159. #478	C₂²×C₃	semidirect
160. #478	C₂²×C₃	semidirect
161. #477	C₂²×C₃	semidirect
162. #476	C₂²×C₃	semidirect
163. #476	C₂²×C₃	semidirect
164. #476	C₂²×C₃	semidirect
165. #475	C₂²×C₃	semidirect
166. #475	C₂²×C₃	semidirect
167. #474	C₂²×C₃	semidirect
168. #474	C₂²×C₃	semidirect
169. #428	C₂²×C₃	semidirect
170. #428	C₂²×C₃	semidirect
171. #427	C₂²×C₃	semidirect
172. C₂×#106	C₂²×C₃	semidirect
173. #424	C₂²×C₃	semidirect
174. #423	C₂²×C₃	semidirect
175. C₂×C₄⋊C₈	C₂²×C₃	semidirect
184. C₃×#41	C₂×Q₈	semidirect
197. C₂×C₃×D₄	C₂×Q₈	semidirect
243. H(5,𝔽₂)	C₃×Q₈	semidirect
357. #41	C₂×C₃×Q₈	semidirect
370. C₂×D₄	C₂×C₃×Q₈	semidirect
499. C₃	#60495	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#3503	2
C₃×C₄×H(5,𝔽₂)	2
C₃×#3084	2
C₃×#3081	2
C₃×#3079	2
C₃×#3077	2
C₃×#3076	2
C₂×C₃×#476	2
C₃×#2912	2
C₃×#2906	2
C₃×#2897	2
#60495	3

Subgroups — C3×#60495 #10679102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60495 #10679102